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class="sidebar-link">什么是平衡二叉树</a></li><li class="sidebar-sub-header"><a href="/front/算法和数据结构/前端算法与数据结构/15.html#为什么有平衡二叉树" class="sidebar-link">为什么有平衡二叉树</a></li><li class="sidebar-sub-header"><a href="/front/算法和数据结构/前端算法与数据结构/15.html#平衡二叉树的判定" class="sidebar-link">平衡二叉树的判定</a></li><li class="sidebar-sub-header"><a href="/front/算法和数据结构/前端算法与数据结构/15.html#平衡二叉树的构造" class="sidebar-link">平衡二叉树的构造</a></li></ul></li><li><a href="/front/算法和数据结构/前端算法与数据结构/16.html" class="sidebar-link">堆结构及其在排序中的应用</a></li><li><a href="/front/算法和数据结构/前端算法与数据结构/17.html" class="sidebar-link">排序算法</a><ul class="sidebar-sub-headers"><li class="sidebar-sub-header"><a href="/front/算法和数据结构/前端算法与数据结构/17.html#冒泡排序" class="sidebar-link">冒泡排序</a></li><li class="sidebar-sub-header"><a href="/front/算法和数据结构/前端算法与数据结构/17.html#插入排序" class="sidebar-link">插入排序</a></li><li class="sidebar-sub-header"><a href="/front/算法和数据结构/前端算法与数据结构/17.html#选择排序" class="sidebar-link">选择排序</a></li><li class="sidebar-sub-header"><a href="/front/算法和数据结构/前端算法与数据结构/17.html#归并排序" class="sidebar-link">归并排序</a></li><li class="sidebar-sub-header"><a href="/front/算法和数据结构/前端算法与数据结构/17.html#快速排序" class="sidebar-link">快速排序</a></li></ul></li><li><a href="/front/算法和数据结构/前端算法与数据结构/18.html" class="sidebar-link">动态规划</a><ul class="sidebar-sub-headers"><li class="sidebar-sub-header"><a href="/front/算法和数据结构/前端算法与数据结构/18.html#爬楼梯" class="sidebar-link">爬楼梯</a></li><li class="sidebar-sub-header"><a href="/front/算法和数据结构/前端算法与数据结构/18.html#最少的硬币数目" class="sidebar-link">最少的硬币数目</a></li></ul></li></ul></section></li></ul> </aside> <main class="page"> <div class="theme-default-content content__default"><h2 id="数组"><a href="#数组" class="header-anchor">#</a> 数组</h2> <h3 id="创建数组"><a href="#创建数组" class="header-anchor">#</a> 创建数组</h3> <p>数组的创建方式：</p> <ol><li>方括号加元素内容</li></ol> <div class="language-js extra-class"><pre class="language-js"><code><span class="token keyword">const</span> arr <span class="token operator">=</span> <span class="token punctuation">[</span><span class="token number">1</span><span class="token punctuation">,</span> <span class="token number">2</span><span class="token punctuation">,</span> <span class="token number">3</span><span class="token punctuation">]</span>
</code></pre></div><ol start="2"><li>构造函数</li></ol> <div class="language-js extra-class"><pre class="language-js"><code><span class="token keyword">const</span> arr <span class="token operator">=</span> <span class="token keyword">new</span> <span class="token class-name">Array</span><span class="token punctuation">(</span><span class="token punctuation">)</span>
</code></pre></div><p>使用构造函数这种方式可以创建指定长度的数组。如下代码创建一个长度为7的数组。</p> <div class="language-js extra-class"><pre class="language-js"><code><span class="token keyword">const</span> arr <span class="token operator">=</span> <span class="token keyword">new</span> <span class="token class-name">Array</span><span class="token punctuation">(</span><span class="token number">7</span><span class="token punctuation">)</span>
</code></pre></div><p>创建一个长度确定、同时每一个元素的值也都确定的数组</p> <div class="language-js extra-class"><pre class="language-js"><code><span class="token keyword">const</span> arr <span class="token operator">=</span> <span class="token keyword">new</span> <span class="token class-name">Array</span><span class="token punctuation">(</span><span class="token number">7</span><span class="token punctuation">)</span><span class="token punctuation">.</span><span class="token function">fill</span><span class="token punctuation">(</span><span class="token number">1</span><span class="token punctuation">)</span>
</code></pre></div><h3 id="访问数组"><a href="#访问数组" class="header-anchor">#</a> 访问数组</h3> <p>可以直接通过索引访问数组元素</p> <div class="language-js extra-class"><pre class="language-js"><code>arr<span class="token punctuation">[</span><span class="token number">0</span><span class="token punctuation">]</span> <span class="token comment">// 访问索引下标为0的元素</span>
</code></pre></div><h3 id="数组的遍历"><a href="#数组的遍历" class="header-anchor">#</a> 数组的遍历</h3> <p>遍历数组的方法有很多，这里我们简单介绍下常用的三个</p> <ol><li>for 循环</li></ol> <div class="language-js extra-class"><pre class="language-js"><code><span class="token comment">// 获取数组的长度</span>
<span class="token keyword">const</span> len <span class="token operator">=</span> arr<span class="token punctuation">.</span>length
<span class="token keyword">for</span><span class="token punctuation">(</span><span class="token keyword">let</span> i<span class="token operator">=</span><span class="token number">0</span><span class="token punctuation">;</span>i<span class="token operator">&lt;</span>len<span class="token punctuation">;</span>i<span class="token operator">++</span><span class="token punctuation">)</span> <span class="token punctuation">{</span>
  <span class="token comment">// 输出数组的元素值，输出当前索引</span>
  console<span class="token punctuation">.</span><span class="token function">log</span><span class="token punctuation">(</span>arr<span class="token punctuation">[</span>i<span class="token punctuation">]</span><span class="token punctuation">,</span> i<span class="token punctuation">)</span>
<span class="token punctuation">}</span>
</code></pre></div><ol start="2"><li>forEach 方法</li></ol> <div class="language-js extra-class"><pre class="language-js"><code>arr<span class="token punctuation">.</span><span class="token function">forEach</span><span class="token punctuation">(</span><span class="token punctuation">(</span><span class="token parameter">item<span class="token punctuation">,</span> index</span><span class="token punctuation">)</span><span class="token operator">=&gt;</span> <span class="token punctuation">{</span>
  <span class="token comment">// 输出数组的元素值，输出当前索引</span>
  console<span class="token punctuation">.</span><span class="token function">log</span><span class="token punctuation">(</span>item<span class="token punctuation">,</span> index<span class="token punctuation">)</span>
<span class="token punctuation">}</span><span class="token punctuation">)</span>
</code></pre></div><ol start="3"><li>map 方法</li></ol> <p>map 方法会根据传入的函数逻辑对数组中每个元素进行处理、进而返回一个全新的数组。</p> <div class="language-js extra-class"><pre class="language-js"><code><span class="token keyword">const</span> newArr <span class="token operator">=</span> arr<span class="token punctuation">.</span><span class="token function">map</span><span class="token punctuation">(</span><span class="token punctuation">(</span><span class="token parameter">item<span class="token punctuation">,</span> index</span><span class="token punctuation">)</span><span class="token operator">=&gt;</span> <span class="token punctuation">{</span>
  <span class="token comment">// 输出数组的元素值，输出当前索引</span>
  console<span class="token punctuation">.</span><span class="token function">log</span><span class="token punctuation">(</span>item<span class="token punctuation">,</span> index<span class="token punctuation">)</span>
  <span class="token comment">// 在当前元素值的基础上加1</span>
  <span class="token keyword">return</span> item<span class="token operator">+</span><span class="token number">1</span>
<span class="token punctuation">}</span><span class="token punctuation">)</span>
</code></pre></div><h3 id="二维数组"><a href="#二维数组" class="header-anchor">#</a> 二维数组</h3> <p>下面是一个二维数组</p> <div class="language-js extra-class"><pre class="language-js"><code><span class="token keyword">const</span> arr <span class="token operator">=</span> <span class="token punctuation">[</span>
  <span class="token punctuation">[</span><span class="token number">1</span><span class="token punctuation">,</span><span class="token number">2</span><span class="token punctuation">,</span><span class="token number">3</span><span class="token punctuation">,</span><span class="token number">4</span><span class="token punctuation">,</span><span class="token number">5</span><span class="token punctuation">]</span><span class="token punctuation">,</span>
  <span class="token punctuation">[</span><span class="token number">1</span><span class="token punctuation">,</span><span class="token number">2</span><span class="token punctuation">,</span><span class="token number">3</span><span class="token punctuation">,</span><span class="token number">4</span><span class="token punctuation">,</span><span class="token number">5</span><span class="token punctuation">]</span><span class="token punctuation">,</span>
  <span class="token punctuation">[</span><span class="token number">1</span><span class="token punctuation">,</span><span class="token number">2</span><span class="token punctuation">,</span><span class="token number">3</span><span class="token punctuation">,</span><span class="token number">4</span><span class="token punctuation">,</span><span class="token number">5</span><span class="token punctuation">]</span><span class="token punctuation">,</span>
  <span class="token punctuation">[</span><span class="token number">1</span><span class="token punctuation">,</span><span class="token number">2</span><span class="token punctuation">,</span><span class="token number">3</span><span class="token punctuation">,</span><span class="token number">4</span><span class="token punctuation">,</span><span class="token number">5</span><span class="token punctuation">]</span><span class="token punctuation">,</span>
  <span class="token punctuation">[</span><span class="token number">1</span><span class="token punctuation">,</span><span class="token number">2</span><span class="token punctuation">,</span><span class="token number">3</span><span class="token punctuation">,</span><span class="token number">4</span><span class="token punctuation">,</span><span class="token number">5</span><span class="token punctuation">]</span>
<span class="token punctuation">]</span>
</code></pre></div><p>在数学中，形如这样长方阵列排列的复数或实数集合，被称为“矩阵”。因此二维数组的别名就叫“矩阵”。</p> <h3 id="二维数组的初始化"><a href="#二维数组的初始化" class="header-anchor">#</a> 二维数组的初始化</h3> <p>推荐的初始化二维数组的方法：</p> <div class="language-js extra-class"><pre class="language-js"><code><span class="token keyword">const</span> len <span class="token operator">=</span> arr<span class="token punctuation">.</span>length
<span class="token keyword">for</span><span class="token punctuation">(</span><span class="token keyword">let</span> i<span class="token operator">=</span><span class="token number">0</span><span class="token punctuation">;</span>i<span class="token operator">&lt;</span>len<span class="token punctuation">;</span>i<span class="token operator">++</span><span class="token punctuation">)</span> <span class="token punctuation">{</span>
  <span class="token comment">// 将数组的每一个坑位初始化为数组</span>
  arr<span class="token punctuation">[</span>i<span class="token punctuation">]</span> <span class="token operator">=</span> <span class="token punctuation">[</span><span class="token punctuation">]</span>
<span class="token punctuation">}</span>
</code></pre></div><p>错误示范：</p> <div class="language-js extra-class"><pre class="language-js"><code><span class="token keyword">const</span> arr <span class="token operator">=</span><span class="token punctuation">(</span><span class="token keyword">new</span> <span class="token class-name">Array</span><span class="token punctuation">(</span><span class="token number">7</span><span class="token punctuation">)</span><span class="token punctuation">)</span><span class="token punctuation">.</span><span class="token function">fill</span><span class="token punctuation">(</span><span class="token punctuation">[</span><span class="token punctuation">]</span><span class="token punctuation">)</span>
</code></pre></div><p>这样乍一看好像没错，但是实际是有问题的</p> <div class="language-js extra-class"><pre class="language-js"><code>arr<span class="token punctuation">[</span><span class="token number">0</span><span class="token punctuation">]</span><span class="token punctuation">[</span><span class="token number">0</span><span class="token punctuation">]</span> <span class="token operator">=</span> <span class="token number">1</span>
</code></pre></div><p><img src="/assets/img/1.9d7884d1.png" alt=""></p> <p>会发现一整列的元素都被设为了 1</p> <p>这是因为当给fill 传递一个入参时，如果这个入参的类型是引用类型，那么 fill 在填充坑位时填充的其实就是入参的引用。</p> <p>上例中的7个数组对应了同一个引用、指向的是同一块内存空间，它们本质上是同一个数组。当修改第0行第0个元素的值时，第1-6行的第0个元素的值也都会跟着发生改变。</p> <h2 id="栈和队列"><a href="#栈和队列" class="header-anchor">#</a> 栈和队列</h2> <p>在JS中我们可以通过数组来实现栈和队列。这里我们先来简单看下数组中增删操作（下面的操作都会改变原数组）：</p> <p>数组中增加元素的三种方法</p> <ol><li>unshift 方法 - 可向数组的开头添加一个或更多元素，并返回新的长度</li></ol> <div class="language-js extra-class"><pre class="language-js"><code><span class="token keyword">const</span> arr <span class="token operator">=</span> <span class="token punctuation">[</span><span class="token number">1</span><span class="token punctuation">,</span><span class="token number">2</span><span class="token punctuation">]</span>
arr<span class="token punctuation">.</span><span class="token function">unshift</span><span class="token punctuation">(</span><span class="token number">0</span><span class="token punctuation">)</span> <span class="token comment">// [0,1,2]</span>
</code></pre></div><ol start="2"><li>push 方法 - 添加元素到数组的尾部，并返回新的长度</li></ol> <div class="language-js extra-class"><pre class="language-js"><code><span class="token keyword">const</span> arr <span class="token operator">=</span> <span class="token punctuation">[</span><span class="token number">1</span><span class="token punctuation">,</span><span class="token number">2</span><span class="token punctuation">]</span>
arr<span class="token punctuation">.</span><span class="token function">push</span><span class="token punctuation">(</span><span class="token number">3</span><span class="token punctuation">)</span> <span class="token comment">// [1,2,3]</span>
</code></pre></div><ol start="3"><li>splice 方法 - 添加元素到数组的指定位置</li></ol> <div class="language-js extra-class"><pre class="language-js"><code><span class="token keyword">const</span> arr <span class="token operator">=</span> <span class="token punctuation">[</span><span class="token number">1</span><span class="token punctuation">,</span><span class="token number">2</span><span class="token punctuation">]</span> 
arr<span class="token punctuation">.</span><span class="token function">splice</span><span class="token punctuation">(</span><span class="token number">1</span><span class="token punctuation">,</span><span class="token number">0</span><span class="token punctuation">,</span><span class="token number">3</span><span class="token punctuation">)</span> <span class="token comment">// [1,3,2]</span>
</code></pre></div><p>数组中删除元素的三种方法</p> <ol><li>shift 方法 - 删除数组头部的元素，并返回删除的元素</li></ol> <div class="language-js extra-class"><pre class="language-js"><code><span class="token keyword">const</span> arr <span class="token operator">=</span> <span class="token punctuation">[</span><span class="token number">1</span><span class="token punctuation">,</span><span class="token number">2</span><span class="token punctuation">,</span><span class="token number">3</span><span class="token punctuation">]</span>
arr<span class="token punctuation">.</span><span class="token function">shift</span><span class="token punctuation">(</span><span class="token punctuation">)</span> <span class="token comment">// [2,3]</span>
</code></pre></div><ol start="2"><li>pop 方法 - 删除数组尾部的元素，并返回删除的元素</li></ol> <div class="language-js extra-class"><pre class="language-js"><code><span class="token keyword">const</span> arr <span class="token operator">=</span> <span class="token punctuation">[</span><span class="token number">1</span><span class="token punctuation">,</span><span class="token number">2</span><span class="token punctuation">,</span><span class="token number">3</span><span class="token punctuation">]</span>
arr<span class="token punctuation">.</span><span class="token function">pop</span><span class="token punctuation">(</span><span class="token punctuation">)</span> <span class="token comment">// [1,2]</span>
</code></pre></div><ol start="3"><li>splice 方法 - 删除数组指定位置的元素，并返回删除的元素的数组</li></ol> <div class="language-js extra-class"><pre class="language-js"><code><span class="token keyword">const</span> arr <span class="token operator">=</span> <span class="token punctuation">[</span><span class="token number">1</span><span class="token punctuation">,</span> <span class="token number">2</span><span class="token punctuation">,</span> <span class="token number">3</span><span class="token punctuation">]</span>
console<span class="token punctuation">.</span><span class="token function">log</span><span class="token punctuation">(</span>arr<span class="token punctuation">.</span><span class="token function">splice</span><span class="token punctuation">(</span><span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">)</span><span class="token punctuation">)</span> <span class="token comment">// [1]</span>
</code></pre></div><p>上面你可能会有疑惑，咦 splice 这个方式是既可以删除元素也可以添加元素的吗，是的，这里简单介绍下 splice 方法。</p> <p>语法：</p> <p>arrayObject.splice(index,howmany,item1,.....,itemX)</p> <p>参数：</p> <ul><li>index	必需。整数，规定添加/删除项目的位置，使用负数可从数组结尾处规定位置。</li> <li>howmany	必需。要删除的项目数量。如果设置为 0，则不会删除项目。</li> <li>item1, ..., itemX	可选。向数组添加的新项目。</li></ul> <p>返回值：</p> <p>包含被删除项目的新数组，如果有的话。</p> <p>从用法可以看出，如果 splice 的第二个参数设置为零，并设置了第三个参数，就会向数组中添加元素，返回结果是一个空数组。</p> <h3 id="栈"><a href="#栈" class="header-anchor">#</a> 栈</h3> <p>栈是一种后进先出(LIFO，Last In First Out)的数据结构。它有两个特征：</p> <ol><li>只允许从尾部添加元素</li> <li>只允许从尾部取出元素</li></ol> <p>在JS中我们可以使用数组的pop和push方法来实现栈这种数据结构。</p> <div class="language-js extra-class"><pre class="language-js"><code><span class="token comment">// 初始状态</span>
<span class="token keyword">const</span> stack <span class="token operator">=</span> <span class="token punctuation">[</span><span class="token punctuation">]</span>

<span class="token comment">// 入栈</span>
stack<span class="token punctuation">.</span><span class="token function">push</span><span class="token punctuation">(</span><span class="token string">'1'</span><span class="token punctuation">)</span>
stack<span class="token punctuation">.</span><span class="token function">push</span><span class="token punctuation">(</span><span class="token string">'2'</span><span class="token punctuation">)</span>
stack<span class="token punctuation">.</span><span class="token function">push</span><span class="token punctuation">(</span><span class="token string">'3'</span><span class="token punctuation">)</span>
stack<span class="token punctuation">.</span><span class="token function">push</span><span class="token punctuation">(</span><span class="token string">'4'</span><span class="token punctuation">)</span>

<span class="token comment">// 出栈</span>
<span class="token keyword">while</span><span class="token punctuation">(</span>stack<span class="token punctuation">.</span>length<span class="token punctuation">)</span> <span class="token punctuation">{</span>
  <span class="token comment">// 访问栈顶元素</span>
  <span class="token keyword">const</span> top <span class="token operator">=</span> stack<span class="token punctuation">[</span>stack<span class="token punctuation">.</span>length <span class="token operator">-</span> <span class="token number">1</span><span class="token punctuation">]</span>
  console<span class="token punctuation">.</span><span class="token function">log</span><span class="token punctuation">(</span><span class="token string">'栈顶为'</span><span class="token punctuation">,</span> top<span class="token punctuation">)</span>

  <span class="token comment">// 栈顶元素出栈</span>
  stack<span class="token punctuation">.</span><span class="token function">pop</span><span class="token punctuation">(</span><span class="token punctuation">)</span>
<span class="token punctuation">}</span>
</code></pre></div><h3 id="队列"><a href="#队列" class="header-anchor">#</a> 队列</h3> <p>队列是一种先进先出（FIFO，First In First Out）的数据结构。它有两个特征：</p> <ol><li>只允许从尾部添加元素</li> <li>只允许从头部移除元素</li></ol> <p>在JS中我们可以通过数组的 push 和 shift 方法来实现队列这种数据结构。</p> <div class="language-js extra-class"><pre class="language-js"><code><span class="token keyword">const</span> queue <span class="token operator">=</span> <span class="token punctuation">[</span><span class="token punctuation">]</span>

queue<span class="token punctuation">.</span><span class="token function">push</span><span class="token punctuation">(</span><span class="token string">'1'</span><span class="token punctuation">)</span>
queue<span class="token punctuation">.</span><span class="token function">push</span><span class="token punctuation">(</span><span class="token string">'2'</span><span class="token punctuation">)</span>
queue<span class="token punctuation">.</span><span class="token function">push</span><span class="token punctuation">(</span><span class="token string">'3'</span><span class="token punctuation">)</span>
queue<span class="token punctuation">.</span><span class="token function">push</span><span class="token punctuation">(</span><span class="token string">'4'</span><span class="token punctuation">)</span>

<span class="token keyword">while</span><span class="token punctuation">(</span>queue<span class="token punctuation">.</span>length<span class="token punctuation">)</span> <span class="token punctuation">{</span>
  <span class="token comment">// 访问队首元素</span>
  <span class="token keyword">const</span> top <span class="token operator">=</span> queue<span class="token punctuation">[</span><span class="token number">0</span><span class="token punctuation">]</span>
  console<span class="token punctuation">.</span><span class="token function">log</span><span class="token punctuation">(</span><span class="token string">'队首元素为'</span><span class="token punctuation">,</span> top<span class="token punctuation">)</span>

  <span class="token comment">// 队首元素出队</span>
  queue<span class="token punctuation">.</span><span class="token function">shift</span><span class="token punctuation">(</span><span class="token punctuation">)</span>
<span class="token punctuation">}</span>
</code></pre></div><h2 id="链表"><a href="#链表" class="header-anchor">#</a> 链表</h2> <p>数组在内存中最为关键的一个特征，就是它一般是对应一段位于自己上界和下界之间的、一段连续的内存空间。</p> <p>链表中的结点，可能是散落在内存空间的各个角落里。</p> <p>在链表中，每一个结点的结构都包括了两部分的内容：数据域和指针域。JS中的链表，是以嵌套的对象的形式实现的：</p> <div class="language-js extra-class"><pre class="language-js"><code><span class="token punctuation">{</span>
  <span class="token comment">// 数据域</span>
  val<span class="token operator">:</span> <span class="token number">1</span><span class="token punctuation">,</span>
  <span class="token comment">// 指针域，指向下一个结点</span>
  next<span class="token operator">:</span> <span class="token punctuation">{</span>
    val<span class="token operator">:</span><span class="token number">2</span><span class="token punctuation">,</span>
    next<span class="token operator">:</span> <span class="token operator">...</span>
  <span class="token punctuation">}</span>
<span class="token punctuation">}</span>
</code></pre></div><p>数据域存储的是当前结点所存储的数据值，而指针域则代表下一个结点（后继结点）的引用。</p> <p><img src="" alt=""></p> <p>当访问链表中的某个节点时，需要从链表的头节点开始逐个访问next，一直访问到目标节点位置。</p> <h3 id="链表结点的创建"><a href="#链表结点的创建" class="header-anchor">#</a> 链表结点的创建</h3> <div class="language-js extra-class"><pre class="language-js"><code><span class="token keyword">function</span> <span class="token function">ListNode</span><span class="token punctuation">(</span><span class="token parameter">val</span><span class="token punctuation">)</span> <span class="token punctuation">{</span>
  <span class="token keyword">this</span><span class="token punctuation">.</span>val <span class="token operator">=</span> val<span class="token punctuation">;</span>
  <span class="token keyword">this</span><span class="token punctuation">.</span>next <span class="token operator">=</span> <span class="token keyword">null</span><span class="token punctuation">;</span>
<span class="token punctuation">}</span>

<span class="token keyword">const</span> node <span class="token operator">=</span> <span class="token keyword">new</span> <span class="token class-name">ListNode</span><span class="token punctuation">(</span><span class="token number">1</span><span class="token punctuation">)</span>  
node<span class="token punctuation">.</span>next <span class="token operator">=</span> <span class="token keyword">new</span> <span class="token class-name">ListNode</span><span class="token punctuation">(</span><span class="token number">2</span><span class="token punctuation">)</span>
</code></pre></div><p>上述代码创建出了一个数据域值为1，next 结点数据域值为2的链表结点：
<img src="" alt=""></p> <h3 id="链表元素的添加"><a href="#链表元素的添加" class="header-anchor">#</a> 链表元素的添加</h3> <p>在链表末尾添加元素</p> <div class="language-js extra-class"><pre class="language-js"><code><span class="token keyword">function</span> <span class="token function">ListNode</span><span class="token punctuation">(</span><span class="token parameter">val</span><span class="token punctuation">)</span> <span class="token punctuation">{</span>
    <span class="token keyword">this</span><span class="token punctuation">.</span>val <span class="token operator">=</span> val
    <span class="token keyword">this</span><span class="token punctuation">.</span>next <span class="token operator">=</span> <span class="token keyword">null</span>
<span class="token punctuation">}</span>

<span class="token keyword">const</span> node1 <span class="token operator">=</span> <span class="token keyword">new</span> <span class="token class-name">ListNode</span><span class="token punctuation">(</span><span class="token number">1</span><span class="token punctuation">)</span>
node1<span class="token punctuation">.</span>next <span class="token operator">=</span> <span class="token keyword">new</span> <span class="token class-name">ListNode</span><span class="token punctuation">(</span><span class="token number">2</span><span class="token punctuation">)</span>
node1<span class="token punctuation">.</span>next<span class="token punctuation">.</span>next <span class="token operator">=</span> <span class="token keyword">new</span> <span class="token class-name">ListNode</span><span class="token punctuation">(</span><span class="token number">3</span><span class="token punctuation">)</span>
</code></pre></div><p><img src="" alt="">
在链表中间添加元素</p> <div class="language-js extra-class"><pre class="language-js"><code><span class="token keyword">function</span> <span class="token function">ListNode</span><span class="token punctuation">(</span><span class="token parameter">val</span><span class="token punctuation">)</span> <span class="token punctuation">{</span>
    <span class="token keyword">this</span><span class="token punctuation">.</span>val <span class="token operator">=</span> val
    <span class="token keyword">this</span><span class="token punctuation">.</span>next <span class="token operator">=</span> <span class="token keyword">null</span>
<span class="token punctuation">}</span>

<span class="token keyword">const</span> node1 <span class="token operator">=</span> <span class="token keyword">new</span> <span class="token class-name">ListNode</span><span class="token punctuation">(</span><span class="token number">1</span><span class="token punctuation">)</span>
node1<span class="token punctuation">.</span>next <span class="token operator">=</span> <span class="token keyword">new</span> <span class="token class-name">ListNode</span><span class="token punctuation">(</span><span class="token number">2</span><span class="token punctuation">)</span>
<span class="token keyword">const</span> node3 <span class="token operator">=</span> <span class="token keyword">new</span> <span class="token class-name">ListNode</span><span class="token punctuation">(</span><span class="token number">3</span><span class="token punctuation">)</span>
node3<span class="token punctuation">.</span>next <span class="token operator">=</span> node1<span class="token punctuation">.</span>next
node1<span class="token punctuation">.</span>next <span class="token operator">=</span> node3
</code></pre></div><p>插入前
<img src="" alt="">
插入后
<img src="" alt=""></p> <h3 id="链表元素的删除"><a href="#链表元素的删除" class="header-anchor">#</a> 链表元素的删除</h3> <div class="custom-block tip"><p class="custom-block-title">注意</p> <p>在删除链表中节点时，重点是定位目标结点的前驱结点。</p></div> <p>这里以删除上例中node3节点为例。</p> <p>删除的方法是直接让它的前驱结点 node1 的 next 指针跳过它、指向 node3 的后继，让其不可能被遍历到，它会被 JS 的垃圾回收器自动回收掉
<img src="" alt=""></p> <div class="language-js extra-class"><pre class="language-js"><code><span class="token keyword">function</span> <span class="token function">ListNode</span><span class="token punctuation">(</span><span class="token parameter">val</span><span class="token punctuation">)</span> <span class="token punctuation">{</span>
  <span class="token keyword">this</span><span class="token punctuation">.</span>val <span class="token operator">=</span> val
  <span class="token keyword">this</span><span class="token punctuation">.</span>next <span class="token operator">=</span> <span class="token keyword">null</span>
<span class="token punctuation">}</span>

<span class="token keyword">const</span> node1 <span class="token operator">=</span> <span class="token keyword">new</span> <span class="token class-name">ListNode</span><span class="token punctuation">(</span><span class="token number">1</span><span class="token punctuation">)</span>
node1<span class="token punctuation">.</span>next <span class="token operator">=</span> <span class="token keyword">new</span> <span class="token class-name">ListNode</span><span class="token punctuation">(</span><span class="token number">2</span><span class="token punctuation">)</span>
<span class="token keyword">const</span> node3 <span class="token operator">=</span> <span class="token keyword">new</span> <span class="token class-name">ListNode</span><span class="token punctuation">(</span><span class="token number">3</span><span class="token punctuation">)</span>
node3<span class="token punctuation">.</span>next <span class="token operator">=</span> node1<span class="token punctuation">.</span>next
node1<span class="token punctuation">.</span>next <span class="token operator">=</span> node3

<span class="token comment">// 删除node3</span>
node1<span class="token punctuation">.</span>next <span class="token operator">=</span> node3<span class="token punctuation">.</span>next
</code></pre></div><h3 id="链表和数组的辨析"><a href="#链表和数组的辨析" class="header-anchor">#</a> 链表和数组的辨析</h3> <p>我们假设数组的长度是 n，那么因增加/删除操作导致需要移动的元素数量，就会随着数组长度 n 的增大而增大，呈一个线性关系。所以说数组增加/删除操作对应的复杂度就是 O(n)</p> <p>链表的优点：添加和删除元素都不需要挪动多余的元素。链表增删操作的复杂度是常数级别的复杂度，用大 O 表示法表示为 O(1)</p> <p>链表的弊端：在访问链表中某个节点时，必须遍历整个链表来查找它。</p> <div class="language-js extra-class"><pre class="language-js"><code><span class="token comment">// 记录目标结点的位置</span>
<span class="token keyword">const</span> index <span class="token operator">=</span> <span class="token number">10</span>  
<span class="token comment">// 设一个游标指向链表第一个结点，从第一个结点开始遍历</span>
<span class="token keyword">let</span> node <span class="token operator">=</span> head  
<span class="token comment">// 反复遍历到第10个结点为止</span>
<span class="token keyword">for</span><span class="token punctuation">(</span><span class="token keyword">let</span> i<span class="token operator">=</span><span class="token number">0</span><span class="token punctuation">;</span>i<span class="token operator">&lt;</span>index<span class="token operator">&amp;&amp;</span>node<span class="token punctuation">;</span>i<span class="token operator">++</span><span class="token punctuation">)</span> <span class="token punctuation">{</span>
    node <span class="token operator">=</span> node<span class="token punctuation">.</span>next
<span class="token punctuation">}</span>
</code></pre></div><p>因此访问链表中指定节点的复杂度为O(n)。而数组因为可以通过索引直接访问指定元素，所以访问数组中指定位置的元素的复杂度为O(1)。</p> <p>还要注意，在真正的数组定义中，都有一个“存储在连续的内存空间里”这样的必要条件。但因为JS中的数组可以存储任何类型的值，所以JS中的数组不一定是连续的内存，如下：</p> <div class="language-js extra-class"><pre class="language-js"><code><span class="token keyword">const</span> arr <span class="token operator">=</span> <span class="token punctuation">[</span><span class="token string">'haha'</span><span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">,</span> <span class="token punctuation">{</span>a<span class="token operator">:</span><span class="token number">1</span><span class="token punctuation">}</span><span class="token punctuation">]</span>
</code></pre></div><p>上面这个数组对应的是一段非连续的内存。此时，JS 数组不再具有数组的特征，其底层使用哈希映射分配内存空间，是由对象链表来实现的。</p> <h2 id="树"><a href="#树" class="header-anchor">#</a> 树</h2> <h3 id="理解树结构"><a href="#理解树结构" class="header-anchor">#</a> 理解树结构</h3> <p><img src="/assets/img/8.3b2af406.png" alt=""></p> <p>这里需要牢记以下几个树的关键特性和重点概念</p> <ol><li>树的层次计算规则：根结点所在的那一层记为第一层，其子结点所在的就是第二层，以此类推</li> <li>结点和树的高度计算规则：叶子结点高度计为1，每向上一层高度就加1，逐层向上累加至目标时，所得到的值就是目标节点的高度。树中节点的最大高度，称为树的高度。</li> <li>度的概念：一个结点开叉出去多少个子树，被记为结点的度。上图中，根结点的度就是3。</li> <li>叶子结点：叶子节点就是度为零的结点。上图中，最后一层的结点的度全部为0，所以这一层的结点都是叶子结点。</li></ol> <h3 id="理解二叉树结构"><a href="#理解二叉树结构" class="header-anchor">#</a> 理解二叉树结构</h3> <div class="custom-block tip"><p class="custom-block-title">注意</p> <p>二叉树不能被简单定义为每个结点的度都是2的树。普通的树并不会区分左子树和右子树，但在二叉树中，左右子树的位置是严格约定、不能交换的。</p></div> <p>二叉树需要满足以下条件：</p> <ol><li>它可以没有根节点，作为一棵空树存在</li> <li>如果它不是空树，那么必须由根结点、左子树和右子树组成，且左右子树都是二叉树。
<img src="/assets/img/9.58edea42.png" alt=""></li></ol> <h3 id="二叉树的编码实现"><a href="#二叉树的编码实现" class="header-anchor">#</a> 二叉树的编码实现</h3> <p>在JS中二叉树使用对象来定义，这个对象由三部分组成：</p> <ul><li>数据域</li> <li>左侧子结点（左子树根结点）的引用</li> <li>右侧子结点（右子树根结点）的引用</li></ul> <p>代码实现：</p> <div class="language-js extra-class"><pre class="language-js"><code><span class="token comment">// 二叉树结点的构造函数</span>
<span class="token keyword">function</span> <span class="token function">TreeNode</span><span class="token punctuation">(</span><span class="token parameter">val</span><span class="token punctuation">)</span> <span class="token punctuation">{</span>
    <span class="token keyword">this</span><span class="token punctuation">.</span>val <span class="token operator">=</span> val<span class="token punctuation">;</span>
    <span class="token keyword">this</span><span class="token punctuation">.</span>left <span class="token operator">=</span> <span class="token keyword">this</span><span class="token punctuation">.</span>right <span class="token operator">=</span> <span class="token keyword">null</span><span class="token punctuation">;</span>
<span class="token punctuation">}</span>

<span class="token keyword">const</span> node  <span class="token operator">=</span> <span class="token keyword">new</span> <span class="token class-name">TreeNode</span><span class="token punctuation">(</span><span class="token number">1</span><span class="token punctuation">)</span>
</code></pre></div><p>一棵二叉树的实际形态：</p> <p><img src="/assets/img/10.bf23652a.png" alt=""></p></div> <footer class="page-edit"><!----> <!----></footer> <div class="page-nav"><p class="inner"><span class="prev">
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